expr bit-wise "or" operator
Arguments must be integers, result is an integer.
Bit n of the result is 0 if bit n of each argument is 0. Otherwise, bit n of the result is 1.
For negative arguments, observe that ~$n==(-1-n) (See the ~ operator for further discussion.) The following cases then exist:
| Case | Result |
|---|---|
| $a>=0, $b>=0 | $a|$b, as defined above. |
| $a>=0, $b<0 | $a|$b == ~(~$a & ~$b) De Morgan's Law |
| == ~(~$a & (-1-$b)) Extended definition of ~ | |
| == -1-(~$a & (-1-$b)) Extended definition of ~ | |
| The expression (-1-$b) is nonnegative, and so the expression (~$a & (-1-$b)) can be evaluated by bitwise operations. | |
| $a<0, $b>=0 | Commute to ($b | $a) and solve as above. |
| $a<0, $b<0 | $a|$b == ~(~$a & ~$b) De Morgan's Law |
| == -1-((-1-$a) & (-1-$b)) Extended definition of ~ | |
| Since (-1-$a) and (-1-$b) are both nonnegative, the & in the expression above can be evaluated wuth bitwise operations. |